parallel mechanism stiffness code
时间: 2024-05-10 21:18:50 浏览: 15
Here is an example code for calculating the stiffness of a parallel mechanism using the finite element method:
```python
import numpy as np
# Define the input parameters
k = 1000 # spring constant
L = 0.1 # length of the strut
theta = np.pi/4 # angle of the strut
delta = 0.01 # displacement
# Define the transformation matrix
T = np.array([[np.cos(theta), -np.sin(theta), 0, L*np.cos(theta)],
[np.sin(theta), np.cos(theta), 0, L*np.sin(theta)],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# Define the stiffness matrix of the strut
k_strut = np.array([[k, 0, 0],
[0, k, 0],
[0, 0, k]])
# Define the global stiffness matrix
K_global = np.zeros((6, 6))
for i in range(3):
for j in range(3):
submat = np.dot(np.dot(T, k_strut[i:i+1, j:j+1]), T.T)
K_global[i:i+1, j:j+1] += submat
K_global[i+3:i+4, j+3:j+4] += submat
# Calculate the displacement vector
u = np.zeros((6, 1))
u[3, 0] = delta
# Calculate the force vector
F = np.dot(K_global, u)
# Calculate the stiffness matrix
K = np.zeros((1, 1))
K[0, 0] = F[3, 0] / delta
```
This code assumes a parallel mechanism consisting of a single strut with a spring constant `k`, a length `L`, and an angle `theta` with respect to the global x-axis. The code calculates the stiffness of the mechanism in the direction of displacement `delta`. The stiffness matrix is calculated using the finite element method, with the transformation matrix `T` used to convert the strut stiffness matrix from local to global coordinates.
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